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A305935 Number of labeled spanning intersecting set-systems on n vertices with no singletons. 3
1, 0, 1, 12, 809, 1146800, 899927167353, 291136684655893185321964, 14704020783497694096988185391720223222562121969, 12553242487939982849962414795232892198542733492886483991398790450208264017757788101836749760 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge. A singleton is an edge containing only one vertex.
LINKS
FORMULA
a(n) = A305843(n) - n * A003465(n-1).
Inverse binomial transform of A306000. - Andrew Howroyd, Aug 12 2019
EXAMPLE
The a(3) = 12 spanning intersecting set-systems with no singletons:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,2,3}}
{{1,3},{1,2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
{{1,2},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
CROSSREFS
Sequence in context: A155813 A220119 A178023 * A228182 A356186 A003748
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 15 2018
EXTENSIONS
a(6)-a(8) from Giovanni Resta, Jun 20 2018
a(9) from Andrew Howroyd, Aug 12 2019
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)